1. Field of the Invention
The present application relates to methods for calibrating sensors for measuring physical parameters in which reading of the sensor varies depending upon conditions such as temperature, so that compensation of the reading from the sensor must be done in order to obtain an accurate value for the measured parameter, and more particularly to calibrating such sensors whose output depends non-linearly on a measured quantity (torque) and on an operating condition (temperature).
2. The Prior Art
The application deals with physical sensors for measuring such quantities as mechanical strain, force, acceleration, pressure, torque, electric and magnetic fields, power, etc. Very often, the sensor reading varies with surrounding conditions, in particular on the ambient temperature, and the only way to compensate this dependence is to measure the temperature along with the physical quantity of interest. In the approach known in the prior art, the sensor is calibrated within the entire working range of temperatures and then the temperature compensated reading is obtained as a result of processing of the information provided by the sensing element in a microprocessor on the basis of a certain calibration model of the sensor.
More particularly, if the aim is to measure the physical quantity M within the range of temperatures T from Tmin to Tmax, the sensing element provides information about M and T in the form of two independently measured physical quantities Fm and Ft. Depending on the sensing technique used they can be currents, voltages (in the case of piezoresistive, piezoelectric, Hall effect, etc. sensors), capacitances (capacitive MEMS sensors), frequencies or time and phase delays (sensors based on resonators and delay lines) and other quantities that can be easily converted into a digital format by electronic circuitry. In general, both Fm and Ft depend on M and T:Fm=Fm(M,T),  (1)Ft=Ft(M,T),  (2)
but their dependencies are different and these dependencies are established by sensor calibration within the temperature range of interest. This produces a calibration model, usually either in the form of look-up tables or in the form of polynomials approximating the actual calibration results. Combinations of both can also be used in order to reduce complexity of the calibration model. For example, if Fm and Ft depend on M linearly or piece-wise linearly, then the following model can be used:
                              F          m                =                  {                                                                                                                                                                  S                          p                                                ⁡                                                  (                          T                          )                                                                    ⁢                      M                                        +                                                                  F                        0                                            ⁡                                              (                        T                        )                                                                              ,                                                                              M                  ≥                  0                                                                                                                                                                                                  S                          n                                                ⁡                                                  (                          T                          )                                                                    ⁢                      M                                        +                                                                  F                        0                                            ⁡                                              (                        T                        )                                                                              ,                                                                                                  M                    <                    0                                    ,                                                                                        (        3        )                                                      F            t                    =                                    a              1                        -                                          a                2                            ⁢              T                        -                                          a                3                            ⁢              M                        +                                          a                4                            ⁢                              T                2                                      +                                          a                5                            ⁢                              T                3                                                    ,                            (        4        )            
where the sensitivities Sp,n and the offset F0 as functions of temperature can be represented by look-up tables in a number of discrete temperature calibration points covering the whole temperature range of interest:
TSpSnF0T1Sp1Sn1F01T2Sp2Sn2F02. . .. . .. . .. . .TnSpnSnnF0n
A practical number of temperature calibration points can be from 10 to 5 for a typical automotive temperature range from −40° C. to +125° C. (it depends on a character of temperature variation of Sp,n and F0). If needed the look-up tables can be expanded on a larger number of points with a smaller temperature step by means of interpolation.
After developing the calibration model, the temperature-compensated value of M, as well as the temperature T, can be found from the sensor readings Fm and Ft by solving simultaneous equations Eqs. (1) and (2) or Eqs. (3) and (4) in the microprocessor.
Any individual physical sensor is fully characterised by a set of calibration parameters, for instance, polynomial coefficients a1-5 and values in the look-up tables Sp1-n, Sn1-n, F01-n.
This prior art approach is fine in theory but has its practical limitations. Individual sensors slightly differ from each other because of fabrication tolerances so that the individual calibration parameters also differ from each other. If the difference is small all the sensors can be described by the same generic calibration parameters a1-5, Sp1-n, Sn1-n, F01-n that can be found as an average of the individual calibration parameters. In this case replacing of the actual individual calibration parameters by the generic ones for a particular sensor does not cause unacceptably large additional errors in the measured value of M. In practice, then, only a first batch of sensors (sufficiently large to be statistically representative) needs to be calibrated within the entire temperature range from Tmin to Tmax in order to find generic calibration parameters. The rest of sensors can be supplied without their calibration just relying on high repeatability of the manufacturing process. This is a standard approach allowing considerable reduction of the sensor cost by excluding a calibration cost from it.
Very often, however, variations in the sensor characteristics are too large to be able to use a single set of generic calibration parameters for all sensors without calibrating them. An example of this situation is demonstrated in FIG. 1, which shows errors in measuring engine output torque by 27 SAW resonant sensors installed on flexplates in the case if their individual calibration parameters are replaced by the generic ones. The curves are plotted against temperature for the measured torque value M=800 Nm, and show that the maximum error exceeds 100% of reading which is obviously unacceptable. In this case the prior art approach is to produce an individual calibration of each sensor within the entire temperature range. Bearing in mind that it needs to be done in relatively large number of temperature points, this process considerably increases the sensor cost. It may even be not feasible in some cases, for instance, if the sensor is installed on a large metal part and needs to be calibrated together with this part. In this case it may take 1-3 hours in order to reach a steady state at each temperature point.